hello all,
i am trying out some of the optimization routines for a problem of mine that is on the form:
min f(x)
s.t M(x) is positive semidefinite
where f is strictly convex in the feasible region with compact sublevel sets, M is linear and takes value in some subspace of hermitian matrices.
the problem is convex but the costraint can not be handled directly by any of the optimization routines in scipy. So i choose to change it to an uncostrained problem with objective function:
f1(x) = f(x) for M(x) pos semi def
f1(x) = Inf otherwise
the problem is that it seems the routines can not handle the infinity values correctly.
Some of the routines (fmin_cg comes to mind) wants to check the gradient at points where the objective function is infinite. Clearly in such cases the gradient is not defined - i.e the calculations fail - and the algorithm terminates.
Others (like fmin_bfgs) strangely converge to a point where the objective is infinite despite the fact that the initial point was not.
Do you have any suggestion to fix this problem?
regards,
Enrico
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